Line tangent to the curve

1. Oct 26, 2008

mbisCool

1. The problem statement, all variables and given/known data

For what values of a and b is the line 3x+y=b tangent to the curve y=ax^3 when x=5 ?

3. The attempt at a solution
I believe i would need to find the equation of the tangent to y=ax^3 when x=5 then that should be equal to -3x+b=y if im not mistaken but im not sure what to do from here to solve for a and b.

Any leads in the right direction or insight if this is the entirely wrong approach would be greatly appreciated!

2. Oct 26, 2008

HallsofIvy

Staff Emeritus
Well, yes, that's just a restatement of the problem! You know that the slope of y= -3x+ b is -3. What connection is there between the slope of a tangent line and the function itself?

3. Oct 26, 2008

mbisCool

thank you for the quick reply hallsofivy. I had -0.04 instead of -3/75 giving me the wrong answer for the online homework webpage which was confusing me. After using -3/75 instead it counts it as correct :(